Equilibrium

∞ generated and posted on 2020.12.19 ∞

Equilibrium is used as a default state for understanding how systems work, though in the case of bodies it is perturbation (existence) away from equilibrium which matters most

To appreciate the concept of equilibrium it is helpful to begin with a teeter totter, i.e., a seesaw. Ignoring the up and down motion, instead consider just the balance between the two sides. That balance, when achieved with neither person's feet on the ground, is an example of an equilibrium. Note that there are two aspects to this equilibrium, the weight of each individual involved and the distance between each of them and the balance point (there is also can be a third component to 'balancing acts', that of the expenditure of energy, which we'll get to a bit later).

Equilibrium is a balancing act, here shown the achievement of a static equilibrium state, by a Volkswagen Beetle!

On a teeter totter, if two individuals do not have the same weight (i.e., mass), then to balance the heavier one needs to sit closer to the balance point (i.e., the fulcrum). This has to do with physics and lever arm lengths, but the important point for us is that the two sides don't have to be identical in all the same ways to be at equilibrium. Instead they can vary in more than one way, with those multiple ways adding up to generate an overall balance between the two sides.

Equilibrium with a lever balances lever arm length with mass.

In chemical equilibrium the equivalent concepts are concentration (as the weight/mass equivalent) and rate constant, which is analogous to distance from the balance point (fulcrum). Thus at chemical equilibrium, rather than weight × lever arm length balancing, it instead is concentration × rate constant that balance. Another way of saying this is that if things take a long time to get going from place A to place B, then they will tend to build up in place A, and particularly so if those same things find it easy to get going from place B back to place A.

These ideas are also equivalent to the concept of handicapping in sports, where performance is evened out by some manner of penalizing the generally better performing individual or team. Make them carry weights while running, ride a bicycle with slower tires, or have to defend a larger goal, whatever. The important point is that you don't have to change both sides equivalently to create a balance between the two sides, that is, to establish an 'equilibrium'.

And so, what about energy? An equilibrium has the property of not requiring inputs of energy for its maintenance. Instead, an equilibrium can be viewed as an energy low, which also represents a stable configuration. Systems tend to move towards equilibrium because the inherent energy found within the system pushes them there, and in the course of this pushing, that energy is lost to the larger environment (i.e., as they say in physics, lost to the rest of the universe). The less energy that a system possesses, then the less it is able to do something, particularly all on its own. The less able something is to change, relying on whatever energy is available to it, then the more stable that something is. Particularly without inputs of additional energy, systems that are found at equilibrium consequently are stable systems.

Alternatively, it is also possible to have balances that do require an input of energy to maintain, and we call those balances steady states. If we return to the teeter-totteranalogy, consider two sides that balance not because they have the same weight or have adjusted their positions relative to the fulcrum but instead because the heavier or more distant individual (or both!) balances their side by pushing against the ground with their feet. In this case what matters are masses, lever arm lengths, and the amount of force being applied to the ground. But since the latter requires an ongoing input of energy, the result is a steady state rather than strictly an equilibrium. For more on these latter ideas, see my essay, Equilibrium and Energy.

Here we consider in particular such steady states in terms of the concept of chemical equilibrium.

First we have to consider how to balance chemical equations. For instance, the following chemical equation is not balanced:

NaCl + CaCO₃ → Na₂CO₃ + CaCl₂ (this is not yet balanced)

To properly balance it, we need to discuss the concept of stoichiometry.

The above video provides a quick introduction to the concept of stoichiometry – hilarious, I think…

Then we turn to reactions rates, which are studies within the context of what are known as reaction kinetics, a.k.a., chemical kinetics.

The above video provides an introduction to the concept of reactions rates.

Next we turn to the issue/concept of reversible reactions such as

2NaCl + CaCO₃ → Na₂CO₃ + CaCl₂ ("Forward")

Na₂CO₃ + CaCl₂ → 2NaCl + CaCO₃ ("Reverse")

Note, by the way, that the above reactions are now properly balanced. We also will consider what are known as equilibrium constants.

Click on this link.

The above video considers reversible reaction equilibria, if we were going to consider the math!

In the above video the equilibrium constant is modified using temperature.

In this video another view of the previous reaction is presented.

The equilibrium constants associated with a hypothetical reversible reaction can be described using two rate constants:

A + B → AB (at rate k₁)
AB → A + B (at rate k₂)

The overall equilibrium constant equals k₁/k₂ (or k₂/k₁ if viewed with the reaction drawn going from right to left rather than left to right).

Related to the idea of reversible reactions, and very important to the functioning of biological systems, is the phenomenon of reversible binding. Particularly, we can distinguish between reversible binding with high versus low affinities between substances. Unfortunately, I have I yet to find any short videos on this subject.